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We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the n th order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some of these distributions are infinitely divisible via Bondesson’s 1979 classifications.

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